2014-07-10 03:41:41 +00:00
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import standard
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namespace setoid
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inductive setoid : Type :=
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2014-07-22 16:43:18 +00:00
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| mk_setoid: Π (A : Type), (A → A → Prop) → setoid
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2014-07-10 03:41:41 +00:00
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definition carrier (s : setoid)
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:= setoid_rec (λ a eq, a) s
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2014-07-22 16:43:18 +00:00
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definition eqv {s : setoid} : carrier s → carrier s → Prop
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2014-07-10 03:41:41 +00:00
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:= setoid_rec (λ a eqv, eqv) s
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infix `≈`:50 := eqv
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coercion carrier
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inductive morphism (s1 s2 : setoid) : Type :=
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| mk_morphism : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism s1 s2
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end
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